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3 years ago

Estimate the percent of each number. 47% of 77

Mathematics

1 answer:

Anettt [7]3 years ago

5 0

ANSWER

36 .19

EXPLANATION

We want to estimate

$47\% \: of \: 77$

This is the same as

$\frac{47}{100} \times 77$

$\frac{47}{100} \times \frac{77}{1}$

We multiply the numerators to get,

$\frac{3619}{100}$

We convert to decimals to get

$36.19$

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Let f(x) = x+2/x+6 <br> f^-1(-6) =

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We can explicitly find the inverse. If $f^{-1}(x)$ is the inverse of $f(x)$ , then

$f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x$

Solve for the inverse :

$\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x$

$\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x$

$1 - \dfrac4{f^{-1}(x) + 6} = x$

$1 - x = \dfrac4{f^{-1}(x) + 6}$

$f^{-1}(x) + 6 = \dfrac4{1-x}$

$\implies f^{-1}(x) = \dfrac4{1-x} - 6$

Then when x = -6, we have

$f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}$

Alternatively, we can first solve for x such that $f(x) = -6$ . Then taking the inverse of both sides, $x = f^{-1}(-6)$ . (The difference in this method is that we don't compute the inverse for all x.)